On nonlinear coupled evolution system with nonlocal subsidiary conditions under fractal‐fractional order derivative

In the given paper, we develop and extend a qualitative analysis of a novel nonlinear system of fractional pantograph evolution differential equations (FPEDEs) involving fractal‐fractional derivative in Atangana‐Baleanu sense. To discuss the proposed problem, we establish the essential conditions for the existence and uniqueness results. The used arguments for the analysis are the fixed point techniques of Banach and Krasnoselskii. Moreover, the Ulam‐Hyers stability of solutions for the system at hand is discussed. Two interesting pertinent examples are presented.